When a note is played or sung by a musician, a sound pressure waveform is established in the air around the musician. The waveform is periodic in time and can ideally be represented by a number of superimposed, interrelated sine waves. One of these waves has a "fundamental" frequency that is perceived as the pitch of the sound. A number of sine waves having frequencies that are integer multiples of the fundamental frequency are also included in the waveform. These additional sine waves are commonly referred to as "harmonics" or "overtones". Even with harmonics present, the pitch of the note is perceived to be the fundamental frequency of the waveform and, therefore, it is this frequency that is of interest.
When two or more musicians perform together, the production of aurally pleasing music is dependent upon the ability of each to produce a range of notes having fundamental frequencies that are substantially the same as those produced by the other musician. Thus, prior to an instrumental performance, it is necessary to tune the instrument, making the minor adjustments necessary to obtain the desired pitch for a particular note played. A device capable of outputting the error in pitch of the note produced can greatly aid the musician in this process.
Given the importance of proper pitch to the performance of music, it is also desirable for a singer or instrumental musician to develop a natural recognition of proper intonation. In this respect, a means for providing immediate feedback regarding intonation has been deemed helpful. For example, it would be quite helpful to a student to be able to continuously monitor intonation problems throughout his or her performance. This monitoring can be performed by the student directly or with the help of computer software when the pitch information is supplied to a computer. Additionally, with immediate intonation feedback available, the information can be input to a synthesizer, which produces an output in response thereto. In this arrangement, the source of the musical note analyzed effectively serves as a keyboard for the synthesizer.
The production of immediate pitch feedback, however, is subject to a number of difficulties. The fundamental frequency of the note played is the inverse of the period of the fundamental sinusoidal component. Thus, if this period can be determined from the waveform, the pitch is readily available. To determine the period, the timing associated with a current point on the waveform must be precisely identified, the period being the time elapsed between repetitions of this reference point. The selection of a suitable reference point, however, is frequently made difficult by the complexity of the waveform involved. As noted earlier, harmonics may be present, producing a number of peaks of varying amplitude for each cycle of the waveform. In addition, the waveform may be subject to periodic amplitude and frequency fluctuations. Even with a suitable reference point selected, the irregularities in the waveform noted may make it difficult to determine the precise time interval elapsed between occurrences of the reference point. The problem of accurate timing is further exaccerbated by the need to produce a determination of pitch over a relatively few cycles of the waveform if the feedback is to be substantially immediate. While a number of devices have been developed in the past to determine the pitch of a note, none has proved fully capable of overcoming these difficulties.
A commonly used reference point for determining the period of the waveform is the zero crossing of the signal. Zero crossings are used, for example, in the electronic tuning aid disclosed by Hollimon (U.S. Pat. No. 4,523,506). For a simple sine wave, the period is easily determined as the time interval between alternate zero crossings of the signal. In addition, because the region of the sine wave having zero amplitude exhibits a relatively high slope, the timing of such zero crossings can be accurately determined. More complex signals, however, can render the zero crossing an unsuitable reference for period detection. For example, the inclusion of harmonics may produce a multitude of zero crossings per cycle, requiring some means for determining which zero crossing indicates the end of the cycle. In addition, waveform complexity may produce a zero crossing region having a relatively low slope, thereby making it difficult to precisely determine the time of the zero crossing and, hence, the period of the signal.
Another common method of determining the period of the fundamental frequency is by using a peak detector circuit responsive to the time interval between peaks of the signal. Peak detection is used, for example, in the apparatus disclosed by Mercer (U.S. Pat. No. 4,273,023). As with zero crossing techniques, peak detection works well with a simple signal, such as a sine wave. When more complex signals are involved, however, the accuracy of peak detection also suffers. For example, the inclusion of harmonics in the signal may produce a number of peaks having similar amplitudes, making it difficult to determine which peak is the reference peak used in measuring the period of the signal. The presence of periodic amplitude fluctuations may similarly affect the accuracy of the method. In addition, the reference peak selected for the signal may also exhibit a relatively low slope, making a precise determination of the timing of the peak difficult to obtain. Thus, an accurate determination of the period is not available.
To overcome some of the problems encountered by zero crossing and peak detection techniques, methods have been developed using the portion of the signal that crosses a set threshold as the reference point for determining the period. For example, in the method and apparatus disclosed by Slepian et al. (U.S. Pat. No. 4,217,808), an automatic gain control device adjusts the positive and negative excursions of the signal to selected levels. Positive and negative thresholds are then established, equal to a percentage of these maximum excursion levels. The period is essentially defined as the time between a first upward crossing of the positive threshold by the signal and a second upward crossing of the positive threshold, separated in time by a downward crossing of the negative threshold. This method of period determination, however, is not without its problems. Like the zero crossing and peak detection techniques, the establishment of a threshold at a predetermined percentage of the maximum peak excursions includes no provision for ensuring that the reference point will correspond to high-slope regions of the signal. Thus, the signal may be relatively low in slope at the threshold crossing, making the exact time of occurrence difficult to ascertain.
Because the timing of the reference points used to determine the period of the signal may be difficult to precisely determine, another technique employs the computation of an average period from a plurality of period measurements as a way of improving accuracy. For example, the note analyzer disclosed by Moravec et al. (U.S. Pat. No. 4,354,418), establishes separate period data counts for a number of cycles of the signal and outputs a period that is an average of the period data counts produced. This system has the disadvantage of making the accuracy of the period determination a function of the number of cycles of the signal analyzed. For apparatus used to provide immediate feedback to musicians, such a technique may be unacceptable.
Prior art techniques have also suggested the establishment of a trial period for comparison with subsequent period measurements. In the note analyzer disclosed by Moravec et al. a target signal is produced that indicates the expected value of the period and rejects subsequent period measurements falling outside a predetermined range of the target signal. When a predetermined number of acceptable period measurements are obtained, the target signal is updated. While this technique has the advantage of further increasing the accuracy and reliability of the period measurement, it does so at the expense of increased measurement time, making immediate feedback to a musician concerning a note played or sung difficult, if not impossible.
For a period determination to be made readily understandable to a musician, reference to the nomenclature of musical notes is typically relied upon. For example, in the apparatus disclosed by Slepian et al., the output is compared with data stored in a look-up table to determine the semitone that the note played is closest to. The note played can then be displayed for the musician.
From the foregoing discussion, it can be appreciated that a pitch detection apparatus capable of producing highly accurate pitch determinations over relatively few cycles of the signal would be most desirable. Heretofore, means relied upon have been unable to produce timing information based upon high-slope regions of the signal whose time can be precisely determined. Thus, the accuracy of individual period determination suffered. Attempts to correct for these inaccuracies by averaging a number of period determinations have required a relatively long measurement time. Thus, the prior art apparently exhibits a tradeoff between accuracy of a given period determination and spontaneity of results.